A Bidirectional Gas Continuation Method for Steady-State Loadability Analysis in Gas Transmission Networks

This article proposes a gas-only continuation framework for steady-state loadability analysis in natural gas transmission networks based on a direction-free reformulation of the General Flow Equation (GFE). The proposed formulation introduces signed pipe flows directly as state variables, thereby representing bidirectionality intrinsically. As a result, flow reversals are handled without switching logic, while the branch geometry and criticality mechanism of the underlying gas-network equilibrium map are preserved. On this basis, a Gas Continuation Method (GCM) is developed to trace equilibrium branches directly in native gas-load space under specified gas-load stress. The method distinguishes the last admissible operating point from the mathematical critical point and incorporates a formal diagnosis to determine whether the detected limiting condition is consistent with a Saddle-Node Bifurcation (SNB). The proposed framework is validated on a three-node benchmark, a realistic Belgian gas transmission network, and a 40-node test system. The results show accurate agreement with Newton–Raphson (NR) solutions in the regular operating regime, robust branch tracing near limiting conditions where standalone NR loses convergence, and consistent handling of signed pipe flows under load-induced flow reversal and under algebraic orientations assigned a priori opposite to the solved physical flow. The Belgian and 40-node cases further show that the operational admissibility limit may precede the mathematical critical point, so pressure-based feasibility and branch-level criticality emerge as related but distinct notions. These features make the proposed methodology a rigorous and practical tool for identifying admissibility limits, interpreting critical behavior, and assessing loadability margins in gas transmission networks.